PhD course: Discrete structures and introduction to proofs

Description

The course is an introduction to the discrete math that computer scientists use. It piggybacks on the new undergraduate course "Discrete structures for computer science" given by Jörn Janneck, but goes into more depth and adds material on interactive proof assistants. If you already have taken a course similar to the undergraduate course (see EDAA40), you cannot get full points for this course.

Form

Read all chapters in the book, except for chapters 5 and 6 (combinatorics and probability).

Do all the exercises in the corresponding chapters.

Attend two video seminars on Coq.

Do the related Coq exercises.

Hand in solutions to End-of-Chapter exercises, and Coq exercises.

Mark exercises from fellow students on one or more chapters.

Advice on exercises and labs

Concerning the exercises: It will be too much work to do and hand in all the End-of-Chapter exercises. Therefore, it is sufficient to hand in 1/4 of them, including the first subexercise of each. Example: In Chapter 1 there are four End-of-Chapter exercises: 1.1, 1.2, 1.3, and 1.4. Of these you should do:

Exercise 1.1 (a), 1.2 (a), 1.3 (a), 1.4 (a)

Since 1.1 has 8 subexercises (a-h), you select one additional, so that you do in total 8/4 = 2 subexercises of 1.1.

For 1.2, which has 11 subexercises (1-k), you should do 11/4 = 3 (after rounding), so you select additionally two subexercises.

Exercises 1.3 and 1.4 have only 3 subexercises each (a-c), so you don't have to do any extra here. The a) is sufficient.

If you select any of the subexercises with subsubexercises, e.g., 1.1 f), which has 4 subsubexercises (i - iv), it is sufficient to select 4/4 = 1 again (i).

Note that you should look at the other exercises too, to convince yourself that you could solve them. But you don't have to write them down and hand them in.

Advice for doing the exercises in Makinson's book. Try to follow the proofs. If you cannot prove something the way the book does it, try drawing a Venn diagram: Name all the different subsets in the diagram, and try to prove the statement that way. If you cannot do this, try to make an argument for why something is true.

Write your solutions for the Makinson exercises using pen and paper, not on the computer. Take a photo of your solution and email it to the marker, and with copy to Görel.

For the labs, email a zip file with your solution to the marker, and with copy to Görel.

For the Coq exercises: email your solved Coq file to the marker, and with copy to Görel.

All exercises and labs should be handed in by the deadline. All marking should be done within one week. Enter the results into the SAM system (PhD course in Discrete Structures).

If there are unclear things, exercises you could not solve, exercises with interesting solutions, let me (Görel) know, and we can gather the group and discuss.